Surface Integral Method for the Second Harmonic Generation in Metal Nanoparticles

TL;DR

This paper introduces a surface integral equation method to evaluate second harmonic generation in arbitrarily shaped metal nanoparticles, accounting for all SH sources and validated against analytical solutions.

Contribution

The paper presents a novel SIE method that includes nonlocal-bulk and local-surface SH sources for complex nanoparticle geometries, advancing SH modeling accuracy.

Findings

Method accurately matches analytical SH-Mie solutions.

Successfully models SH scattering in complex-shaped nanoparticles.

Enables improved design of nanoplasmonic devices with enhanced SH emission.

Abstract

Second harmonic (SH) radiation in metal nanoparticles is generated by both nonlocal-bulk and local-surface SH sources, induced by the electromagnetic field at the fundamental frequency. We propose a surface integral equation (SIE) method for evaluating the SH radiation generated by metal nanoparticles with arbitrary shapes, considering all SH sources. We demonstrate that the contribution of the nonlocal-bulk SH sources to the SH electromagnetic field can be taken into account through equivalent surface electric and magnetic currents. We numerically solve the SIE problem by using the Galerkin method and the Rao-Wilton-Glisson basis functions in the framework of the distribution theory. The accuracy of the proposed method is verified by comparison with the SH-Mie analytical solution. As an example of a complex-shaped particle, we investigate the SH scattering by a triangular nano-prism. This method paves the way for a better understanding of the SH generation process in arbitrarily shaped nanoparticles and can also have a high impact in the design of novel nanoplasmonic devices with enhanced SH emission.